Ministers hope to assuage critics of the government's plan for childcare vouchers by extending the £1,200 tax-free scheme to parents who stay at home because they are carers, and to parents on maternity or paternity leave.

The government hopes the two concessions, to be announced on Monday, will do something to see off critics who claim the new vouchers punish families where one parent stays at home.

In March, it was announced that the voucher would only be available to households where both parents are at work, prompting criticism that the government was punishing stay-at-home parents. The Pre-School Learning Alliance said the plans were unfair, and that they flew in the face of the pre-election rhetoric to help mothers who stayed at home.

Neil Leitch, chief executive of the alliance said: "To offer this money to a couple whose dual earnings could reach £300,000 but not to a couple earning a fraction of this amount who choose to have one parent stay at home seems perverse. This seems to be more about dangling a £1,200 carrot to tempt mums back to work rather than providing real childcare choices."

The Treasury claims such criticism is a misunderstanding of the scheme, which is aimed at reducing costs of childcare so that it becomes financially more worthwhile for more parents to go to work or to stay in work.

Extortionate childcare costs are often cited as one of the chief reasons why both parents do not go to work.

The changes are to be announced as part of a three-month consultation launched on Monday on the childcare package designed eventually to help with the childcare costs of children aged up to 12.

Any family where both parents are in work and each is earning less than £150,000 will be eligible.

The scheme will take many years to be fully operational since it will be phased in from autumn 2015. Families with children aged under five are initially covered. The payment will start at the beginning of the school year, and will eventually cover 2.5 million working families.

The scheme could save a typical family with two children aged under 12 up to £2,400 a year. The average cost of a part-time nursery place for a child under two in the UK is now more than £5,000 per year, or £4.34 an hour.

Ministers say they want feedback from parents for their plans. A simple online version of the 12-week consultation has been prepared for parents by the Treasury.

A recent coalition consultation on childcare – over relaxing the ratios between children and nursery staff – ended disastrously for the Conservatives as the Liberal Democrats withdrew support for the plan, citing a parent backlash during the consultation.

Some Conservatives blamed the organisation Mumsnet for orchestrating the opposition, and the Treasury is trying to organise this consultation so parents respond directly to the Treasury, a move possibly intended to reduce the influence of lobbying groups.

George Osborne, who is due to visit a nursery on Monday, said: "This government is on the side of people who want to work hard and get on in life. Tax-free childcare will help working parents by giving them more choice and better access to the quality, affordable childcare they need.

"We want to make the new scheme work in the way that is best for parents, so today we are asking for their views, and I'd like as many parents as possible to tell us what they think."

Under the scheme, parents will be able to open an online voucher account with a provider and have their payments topped up by the government. The vouchers can then be redeemed against childcare from any Ofsted-registered provider.

The new regime will mean the phasing out of the employer-backed childcare system. At present, about 5% of employers opt in, covering around 500,000 households. Parents can pay directly for some childcare out of their gross annual wage, giving relief from income tax and national insurance costs.

Nick Clegg has been attacked about the impact of the proposals on stay at home mothers on his weekly LBC radio phone-in.

Laura Perrins, a barrister, told the deputy prime minister: "I'm just wondering why the coalition is discriminating against mothers like me who care for their children at home. You probably think what I do is a worthless."

Clegg pointed to the help that the government was already giving with childcare, including 15 hours of free pre-school support given to 40% of the most disadvantaged two year olds.

He defended the eligibility of the voucher scheme arguing: "What we are saying is that there are people who would like to work. So that's the choice that they would like to take, but they can't because childcare costs are so high."